What is the radius of the circle with equation (x+7)2+(y-4)2=11?



The general equation of a circle is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle, and \(r\) is the radius.

In the given equation:
\[
(x + 7)^2 + (y - 4)^2 = 11
\]

This can be rewritten as:
\[
(x - (-7))^2 + (y - 4)^2 = 11
\]

From this, we can see that:
- The center of the circle is \((-7, 4)\)
- The value \(r^2 = 11\), so the radius \(r = \sqrt{11}\)

Therefore, the radius of the circle is \(\sqrt{11}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the center of a circle from its equation?
2. What is the equation of a circle with radius 5 and center at (3, -2)?
3. How do you calculate the area of a circle given its radius?
4. How would the equation change if the radius doubled?
5. Can you derive the equation of a circle from its diameter?

**Tip:** Always compare your circle equation with the standard form to easily identify the center and radius.

What is the radius of the circle with equation (x+7)^2+(y-4)^2=11?

Learn how to determine the radius of a circle from its equation (x+7)^2 + (y-4)^2 = 11. Understand the standard form of a circle's equation, identify its center, and calculate the radius using square root. Suitable for students in Grades 9-10 studying geometry and coordinate geometry.

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